Side Angle Side Postulate

The Side Angle Side postulate (often abbreviated as SAS) states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then these two triangles are congruent.

$$ \triangle ABC \cong \triangle XYZ $$
• Two sides and the included angle are congruent
  • AC = ZX  (side)
  • $$ \angle $$ACB = $$ \angle $$XZY  (angle)
  • CB = ZY   (side)
• Therefore, by the Side Angle Side postulate, the triangles are congruent.

The included angle means the angle between two sides. In other words it is the angle 'included between' two sides.

Identify Side Angle Side Relationships

In which pair of triangles pictured below could you use the Side Angle Side postulate (SAS) to prove the triangles are congruent?

Answer

Pair four is the only true example of this method for proving triangles congruent. It is the only pair in which the angle is an included angle.

Given: 1) point C is the midpoint of BF 2) AC= CE

Prove that $$ \triangle ABC \cong \triangle $$EFC

Side Angle Side Example Proof

Prove $$ \triangle BCD \cong \triangle BAD $$

Given: HJ is a perpendicular bisector of KI

Side Angle Side Activity

Below is the proof that two triangles are congruent by Side Angle Side.

Can you imagine or draw on a piece of paper, two triangles, $$ \triangle BCA \cong \triangle XCY $$ , whose diagram would be consistent with the Side Angle Side proof shown below?

Show Two Triangles